Question

How do you factor n^2-4n=0

Answer 1

To factor the equation n^2 - 4n = 0, we factor out the common 'n' resulting in n(n - 4) = 0, which gives us two possible solutions: n = 0 and n = 4.

Step-by-step explanation:

To factor the quadratic equation n^2 - 4n = 0, we look for common factors in both terms. We notice that 'n' is a common factor and can be factored out, giving us n(n - 4) = 0. This means that either n = 0 or n - 4 = 0, leading us to the solutions n = 0 or n = 4.

To understand the properties of exponents used in factoring, recall that a number raised to the fourth power equals that number multiplied by itself four times. The expression n^2, for example, represents that 'n' is multiplied by itself to give n x n.

When factoring quadratic equations of the form at^2 + bt + c = 0, the fundamentals of factoring are applied to simplify and solve for 't'. However, in the simpler equation n^2 - 4n = 0, straightforward factoring is sufficient to solve for 'n'.

Answer 2

n² - 4n = 0
n(n) - n(4) = 0
n(n - 4) = 0
n = 0 or n - 4 = 0
+ 4 + 4
n = 4

Solution Set: {0, 4}